When driving off on a slope which is inclined upward in the direction of travel (uphill slope), a driver is often able to estimate, based on experience, the engine torque to be set using the accelerator in order to drive off.
If, however, there are different coefficients of friction on this slope between the right and left sides of the vehicle (split-μ uphill slope), then driving off the vehicle without traction aid is almost impossible for a corresponding slope, since the wheel on the side of the lower coefficient of friction starts spinning. Depending on the gradient, the vehicle may even roll backward on the slope.
When driving off on a split-μ uphill slope using traction aid (e.g., TCS) the driver must set a higher engine torque to drive off the vehicle. The spinning wheel on the low-μ side is braked by the TCS (traction control system) via the brake intervention, and a driving torque of the magnitude of the braking torque is transmitted to the wheel situated on the high-μ side, making it possible to drive the vehicle forward. This transmission of the driving torque is an effect of the coupling of the wheels via a differential. The required braking torque (locking torque) on the low-μ side must be applied via the driver's action as an additional engine torque.
Since the driver is often not aware of these physical relationships when driving off on a split-μ uphill slope, the driver relies on intuition and sets an engine torque that is too low. Upon noticing that the vehicle does not start moving, the driver gradually increases the torque until the vehicle starts moving.
If the driving torque set is so low that the wheel on the low-μ side does not immediately run with a high degree of slip, the pressure builds up hesitantly, resulting in the vehicle starting to roll backward. To prevent it from rolling backward, the driver must quickly give more gas to increase the driving torque and consequently the locking torque (via the TCS brake intervention). This response, however, is unnatural to the driver who, instead of giving more gas, will be startled and actuate the brake, interrupting the drive-off sequence.
Roll-back may also occur if the braking torque (locking torque) is built up with a delay due to wheel vibrations. At low temperatures brake pressure buildup also often does not take place quickly enough to prevent the vehicle from rolling backward.